Which of the following numbers is a factor of 165? ${8,9,10,11,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $165$ by each of our answer choices. $165 \div 8 = 20\text{ R }5$ $165 \div 9 = 18\text{ R }3$ $165 \div 10 = 16\text{ R }5$ $165 \div 11 = 15$ $165 \div 14 = 11\text{ R }11$ The only answer choice that divides into $165$ with no remainder is $11$ $ 15$ $11$ $165$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $165$ $165 = 3\times5\times11 11 = 11$ Therefore the only factor of $165$ out of our choices is $11$. We can say that $165$ is divisible by $11$.